Huizhou resident population, Guangdong resident population and elderly population forecast based on the NAR neural network Markov model

Dewang Li; Meilan Qiu; Zhongliang Luo; Dewang Li; Meilan Qiu; Zhongliang Luo

doi:10.3934/math.2024157

AIMS Mathematics

2024, Volume 9, Issue 2: 3235-3252. doi: 10.3934/math.2024157

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Huizhou resident population, Guangdong resident population and elderly population forecast based on the NAR neural network Markov model

1.
School of Mathematics and Statistics, Huizhou University, Huizhou 516007, China
2.
School of Electronic and Information Engineering, Huizhou University, Huizhou 516007, China

Received: 31 October 2023 Revised: 13 December 2023 Accepted: 18 December 2023 Published: 03 January 2024
MSC : 62M05, 62M10, 62P05, 62P20

We propose a nonlinear auto regressive neural network Markov model (NARMKM) to predict the annual Huizhou resident population, Guangdong resident population and elderly population in China, and improve the accuracy of population forecasting. The new model is built upon the traditional neural network model and utilized matrix perturbation theory to study the natural and response characteristics of a system when the structural parameters change slightly. The delay order and hidden layer number of neurons has a greater effect the prediction result of NAR neural network model. Therefore, we make full use of prior information to constrain and test when making predictions. We choose reasonable parameter settings to obtain more reliable prediction results. Three experiments are conducted to validate the high prediction accuracy of the NARMKM model, with mean absolute percentage error (MAPE), root mean square error (RMSE), STD and R². These results demonstrate the superior fitting performance of the NARMKM model when compared to other six competitive models, including GM (1, 1), ARIMA, Multiple regression, FGM (1, 1), FANGBM and NAR. Our study provides a scientific basis and technical references for further research in the finance as well as population fields.
- NAR,
- neural network,
- fractional grey models,
- machine learning,
- parameter estimation and prediction,
- stochastic Markov process,
- time series
Citation: Dewang Li, Meilan Qiu, Zhongliang Luo. Huizhou resident population, Guangdong resident population and elderly population forecast based on the NAR neural network Markov model[J]. AIMS Mathematics, 2024, 9(2): 3235-3252. doi: 10.3934/math.2024157

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Abstract

We propose a nonlinear auto regressive neural network Markov model (NARMKM) to predict the annual Huizhou resident population, Guangdong resident population and elderly population in China, and improve the accuracy of population forecasting. The new model is built upon the traditional neural network model and utilized matrix perturbation theory to study the natural and response characteristics of a system when the structural parameters change slightly. The delay order and hidden layer number of neurons has a greater effect the prediction result of NAR neural network model. Therefore, we make full use of prior information to constrain and test when making predictions. We choose reasonable parameter settings to obtain more reliable prediction results. Three experiments are conducted to validate the high prediction accuracy of the NARMKM model, with mean absolute percentage error (MAPE), root mean square error (RMSE), STD and R². These results demonstrate the superior fitting performance of the NARMKM model when compared to other six competitive models, including GM (1, 1), ARIMA, Multiple regression, FGM (1, 1), FANGBM and NAR. Our study provides a scientific basis and technical references for further research in the finance as well as population fields.

References

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